Application of high-order finite-element method to the P-wave propagation around and inside an underground cavity

We have studied the scattering of P-waves from an acoustic inclusion in a 2D half-space with a free surface. The motivation for our study comes from detecting a cavity that might be caused by an underground nuclear explosion. This is relevant to on-site inspections, an element of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The waveform modeling we address is implemented in the frequency domain; i.e., we consider the wavefield as well as the source to be time harmonic. We numerically investigate the cases in which the source of the scattered field is either a plane wave from the bottom or the side as from passive sources, such as teleseismic waves or ambient noise, or a spherical wave from the surface as from an active point source, such as a vibroseis or an explosion. To this end, we split the total field in an incident and an unknown scattered field to understand the effects more explicitly. Modeling the response of a void in a medium is not trivial, and many numerical algorithms commonly used for seismic propagation modeling will fail. Therefore, we want to highlight the advantage of high-order methods for this type of application in general and reveal the benefit of using the finite-element method code Ngsolve. This is in particular the case for the situation we have at hand, in which the ratio between the size and the depth of the cavity is notably high. We have addressed this scenario numerically for the first time because there are few field observations of the effects and the number of papers addressing the theoretical basis is sparse. Finally, we found that our splitting strategy together with the numerical scheme that we apply give rise to a constructive approach for studying this specific issue.